scholarly journals Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates

2019 ◽  
Vol 33 (8) ◽  
pp. 3719-3765 ◽  
Author(s):  
Andrea Ajello ◽  
Luca Benzoni ◽  
Olena Chyruk
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Real Term ◽  
No Arbitrage ◽  
Market Participants ◽  
Oxford University ◽  
Term Structures ◽  
Consumer Prices ◽  
Real Risk ◽  
Pass Through

Abstract We propose a no-arbitrage model of the nominal and real term structures that accommodates the different persistence and volatility of distinct inflation components. Core, food, and energy inflation combine into a single total inflation measure that ties nominal and real risk-free bond prices together. The model successfully extracts market participants’ expectations of future inflation from nominal yields and inflation data. Estimation uncovers a factor structure common to core inflation and interest rates and downplays the pass-through effect of short-lived food and energy shocks on inflation and interest rates. Model forecasts systematically outperform survey forecasts and other benchmarks. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Yield Curves, Swap Curves, and Term Structure of Interest Rates

2019 ◽  
pp. 203-228
Author(s):  
Tom P. Davis ◽  
Dmitri Mossessian
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Yield Curves ◽  
No Arbitrage ◽  
Interest Rate Swap ◽  
The Interest Rate ◽  
Rate Swap ◽  
The U.S

This chapter discusses multiple definitions of the yield curve and provides a conceptual understanding on the construction of yield curves for several markets. It reviews several definitions of the yield curve and examines the basic principles of the arbitrage-free pricing as they apply to yield curve construction. The chapter also reviews cases in which the no-arbitrage assumption is dropped from the yield curve, and then moves to specifics of the arbitrage-free curve construction for bond and swap markets. The concepts of equilibrium and market curves are introduced. The details of construction of both types of the curve are illustrated with examples from the U.S. Treasury market and the U.S. interest rate swap market. The chapter concludes by examining the major changes to the swap curve construction process caused by the financial crisis of 2007–2008 that made a profound impact on the interest rate swap markets.

scholarly journals GENERAL ANALYSIS OF LONG-TERM INTEREST RATES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050002
Author(s):  
FRANCESCA BIAGINI ◽  
ALESSANDRO GNOATTO ◽  
MAXIMILIAN HÄRTEL
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Applied Mathematics ◽  
Mathematical Finance ◽  
Rational Model ◽  
No Arbitrage ◽  
Working Paper ◽  
Social Discounting ◽  
The Relationship

We introduce here the idea of a long-term swap rate, characterized as the fair rate of an overnight indexed swap (OIS) with infinitely many exchanges. Furthermore, we analyze the relationship between the long-term swap rate, the long-term yield, (F. Biagini, A. Gnoatto & M. Härtel (2018) Affine HJM Framework on [Formula: see text] and long-term yield, Applied Mathematics and Optimization 77 (3), 405–441, F. Biagini & M. Härtel (2014) Behavior of long-term yields in a lévy term structure, International Journal of Theoretical and Applied Finance 17 (3), 1–24, N. El Karoui, A. Frachot & H. Geman (1997) A note on the behavior of long zero coupon rates in a no arbitrage framework. Working Paper. Available at Researchgate: https://www.researchgate.net/publication/5066730) , and the long-term simple rate (D. C. Brody & L. P. Hughston (2016) Social discounting and the long rate of interest, Mathematical Finance 28 (1), 306–334) as long-term discounting rate. Finally, we investigate the existence of these long-term rates in two-term structure methodologies, the Flesaker–Hughston model and the linear-rational model. A numerical example illustrates how our results can be used to estimate the nonoptional component of a CoCo bond.

scholarly journals Forecasting the Term Structure of Interest Rates with Dynamic Constrained Smoothing B-Splines

2020 ◽  
Vol 13 (4) ◽  
pp. 65
Author(s):  
Eduardo Mineo ◽  
Airlane Pereira Alencar ◽  
Marcelo Moura ◽  
Antonio Elias Fabris
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Parametric Models ◽  
Parametric Curve ◽  
Middle Term ◽  
No Arbitrage ◽  
B Splines ◽  
Curve Model ◽  
Mean Square Errors

The Nelson–Siegel framework published by Diebold and Li created an important benchmark and originated several works in the literature of forecasting the term structure of interest rates. However, these frameworks were built on the top of a parametric curve model that may lead to poor fitting for sensible term structure shapes affecting forecast results. We propose DCOBS with no-arbitrage restrictions, a dynamic constrained smoothing B-splines yield curve model. Even though DCOBS may provide more volatile forward curves than parametric models, they are still more accurate than those from Nelson–Siegel frameworks. DCOBS has been evaluated for ten years of US Daily Treasury Yield Curve Rates, and it is consistent with stylized facts of yield curves. DCOBS has great predictability power, especially in short and middle-term forecast, and has shown greater stability and lower root mean square errors than an Arbitrage-Free Nelson–Siegel model.

A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES

2007 ◽  
Vol 10 (01) ◽  
pp. 155-202 ◽  
Author(s):  
CARL CHIARELLA ◽  
CHRISTINA NIKITOPOULOS SKLIBOSIOS ◽  
ERIK SCHLÖGL
Keyword(s):  
Diffusion Process ◽  
Interest Rates ◽  
Term Structure ◽  
Forward Rate ◽  
Term Structure Model ◽  
Forward Rates ◽  
Defaultable Bond ◽  
Term Structures ◽  
State Dependent ◽  
Path Independence

The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

scholarly journals Beauty Contests and the Term Structure

2021 ◽  
Author(s):  
Martin Ellison ◽  
Andreas Tischbirek
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Aggregate Demand ◽  
Significant Proportion ◽  
Real Term ◽  
Quantitative Model ◽  
Discount Factors ◽  
Stochastic Discount Factors ◽  
Beauty Contest ◽  
Term Premia

Abstract A novel decomposition highlights the scope for information to influence the term structure of interest rates. Based on the law of total covariance, we show that real term premia in macroeconomic models contain a component that depends on covariances of realised stochastic discount factors and a component that depends on covariances of expectations of those stochastic discount factors. The covariance of expectations is typically low in macro-finance models, which contributes to the real term premia implied by the models being at least an order of magnitude too small, a result that is unchanged even if we introduce aggregate demand externalities combined with shocks to higher-order beliefs. We argue that generating realistic term premia requires there to be strategic complementarities in the formation of expectations. A quantitative model, in which beliefs are formed in a beauty contest, can explain a significant proportion of observed term premia, when estimated using data on expectations of productivity growth from the Survey of Professional Forecasters.

The Term Structure of Interest Rates and the Evaluation of Forestry Investments: A Note

1988 ◽  
Vol 12 (4) ◽  
pp. 256-258
Author(s):  
F. Christian Zinkhan
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Discount Rate ◽  
Net Present Value ◽  
Present Value ◽  
Term Structures ◽  
Forestry Investments ◽  
The Relationship

Abstract The forestry literature generally assumes that the appropriate discount rate to be used in the estimation of a given investment's net present value is the same over its lifetime. However, the values of many alternative investments such as stocks and bonds often reflect term structures that are not flat. That is, the relationship between the number of years to maturity of an investment and that investment's required rate of return is often a significant consideration. This note suggests a procedure for incorporating a consideration of the term structure of interest rates into the determination of a discount rate specific to each annual net cash flow associated with a given long-term forestry investment. Using an actual 10-year case analysis, it was found that the valuation of a timberland tract varied by approximately 11%, depending upon whether or not the term structure of interest rates was recognized. South. J. Appl. For. 12(4):256-258.

A yield-only model for the term structure of interest rates

2013 ◽  
Vol 8 (1) ◽  
pp. 99-130 ◽  
Author(s):  
Şule Şahin ◽  
Andrew J.G. Cairns ◽  
Torsten Kleinow ◽  
A. David Wilkie
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Principal Components ◽  
Missing Values ◽  
Yield Curve ◽  
Principal Component ◽  
Data Bank ◽  
Term Structure Model ◽  
Term Structures ◽  
Bank Of England

AbstractThis paper develops a term structure model for the UK nominal, real and implied inflation spot zero-coupon rates simultaneously. We start with fitting a descriptive yield curve model proposed by Cairns (1998) to fill the missing values for certain given days at certain maturities in the yield curve data provided by the Bank of England. We compare four different fixed ‘exponential rate’ parameter sets and decide the set of parameters which fits the data best. With the chosen set of parameters we fit the Cairns model to the daily values of the term structures. By applying principal component analysis on the hybrid data (Bank of England data and fitted spot rates for the missing values) we find three principal components, which can be described as ‘level’, ‘slope’ and ‘curvature’, for each of these series. We explore the relation between these principal components to construct a ‘yield-only’ model for actuarial applications. Main contribution of this paper is that the models developed in the paper enable the practitioners to forecast three term structures simultaneously and it also provides the forecast for whole term structures rather than just short and long end of the yield curves.

scholarly journals Term Structure Estimation with Survey Data on Interest Rate Forecasts

2011 ◽  
Vol 47 (1) ◽  
pp. 241-272 ◽  
Author(s):  
Don H. Kim ◽  
Athanasios Orphanides
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Market Price ◽  
Gaussian Model ◽  
Small Sample ◽  
Expectations Hypothesis ◽  
No Arbitrage ◽  
Short Run ◽  
Small Sample Problem

AbstractThe estimation of dynamic no-arbitrage term structure models with a flexible specification of the market price of risk is beset by severe small-sample problems arising from the highly persistent nature of interest rates. We propose using survey forecasts of a short-term interest rate as an additional input to the estimation to overcome the problem. To illustrate the methodology, we estimate the 3-factor affine-Gaussian model with U.S. Treasury yields data and demonstrate that incorporating information from survey forecasts mitigates the small-sample problem. The model thus estimated for the 1990–2003 sample generates a stable and sensible estimate of the expected path of the short rate, reproduces the well-known stylized patterns in the expectations hypothesis tests, and captures some of the short-run variations in the survey forecast of the changes in longer-term interest rates.

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